LEADER 04070nam 22006495 450 001 9910728930903321 005 20240619101849.0 010 $a3-031-20409-3 024 7 $a10.1007/978-3-031-20409-8 035 $a(MiAaPQ)EBC30589503 035 $a(Au-PeEL)EBL30589503 035 $a(DE-He213)978-3-031-20409-8 035 $a(PPN)272261009 035 $a(CKB)26869083000041 035 $a(EXLCZ)9926869083000041 100 $a20230607d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMultiscale Model Reduction $eMultiscale Finite Element Methods and Their Generalizations /$fby Eric Chung, Yalchin Efendiev, Thomas Y. Hou 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (499 pages) 225 1 $aApplied Mathematical Sciences,$x2196-968X ;$v212 311 08$aPrint version: Chung, Eric Multiscale Model Reduction Cham : Springer International Publishing AG,c2023 9783031204081 327 $aIntroduction -- Homogenization and Numerical Homogenization of Linear Equations -- Local Model Reduction: Introduction to Multiscale Finite Element Methods -- Generalized Multiscale Finite Element Methods: Main Concepts and Overview -- Adaptive Strategies -- Selected Global Formulations for GMsFEM and Energy Stable Oversampling -- GMsFEM Using Sparsity in the Snapshot Spaces -- Space-time GMsFEM -- Constraint Energy Minimizing Concepts -- Non-local Multicontinua Upscaling -- Space-time GMsFEM -- Multiscale Methods for Perforated Domains -- Multiscale Stabilization -- GMsFEM for Selected Applications -- Homogenization and Numerical Homogenization of Nonlinear Equations -- GMsFEM for Nonlinear Problems -- Nonlinear Non-local Multicontinua Upscaling -- Global-local Multiscale Model Reduction Using GMsFEM -- Multiscale Methods in Temporal Splitting. Efficient Implicit-explicit Methods for Multiscale Problems -- References -- Index. 330 $aThis monograph is devoted to the study of multiscale model reduction methods from the point of view of multiscale finite element methods. Multiscale numerical methods have become popular tools for modeling processes with multiple scales. These methods allow reducing the degrees of freedom based on local offline computations. Moreover, these methods allow deriving rigorous macroscopic equations for multiscale problems without scale separation and high contrast. Multiscale methods are also used to design efficient solvers. This book offers a combination of analytical and numerical methods designed for solving multiscale problems. The book mostly focuses on methods that are based on multiscale finite element methods. Both applications and theoretical developments in this field are presented. The book is suitable for graduate students and researchers, who are interested in this topic. 410 0$aApplied Mathematical Sciences,$x2196-968X ;$v212 606 $aNumerical analysis 606 $aMathematics?Data processing 606 $aMathematical physics 606 $aNumerical Analysis 606 $aComputational Science and Engineering 606 $aTheoretical, Mathematical and Computational Physics 606 $aModelització multiescala$2thub 608 $aLlibres electrònics$2thub 615 0$aNumerical analysis. 615 0$aMathematics?Data processing. 615 0$aMathematical physics. 615 14$aNumerical Analysis. 615 24$aComputational Science and Engineering. 615 24$aTheoretical, Mathematical and Computational Physics. 615 7$aModelització multiescala 676 $a511.8 676 $a511.8 700 $aChung$b Eric$01365639 701 $aEfendiev$b Yalchin$0472316 701 $aHou$b Thomas Y$0504781 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910728930903321 996 $aMultiscale Model Reduction$93387810 997 $aUNINA